f be a real function such that f(x+y) =f(x)f(y). If f(1) = a, what is the valueof f(50) ?

Question

f be a real function such that f(x+y) =f(x)f(y). If f(1) = a, what is the valueof f(50) ?
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Solution 1

The function f(x+y) = f(x)f(y) is known as a Cauchy functional equation.

Given that f(1) = a, we can find the value of f(50) by using the property of the function repeatedly.

Step 1: We know that f(1) = a.

Step 2: We can express 50 as 1+1+1+...+1 (50 times).

Step 3: Using the property f(x+y) Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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